Shiny App: Bayesian Analysis of Normal Data

[giankdiluvi]

• AUTHOR(S): Gian Carlo Diluvi
• TITLE: Bayesian Analysis of Normal Data
• MAIN TOPIC: Interactive Bayesian inference
• DESCRIPTION: Learn more about Bayesian inference, including prior specification and posterior analysis, for Normal data using an interactive online resource.
• LINK TO DEPLOYED APP: https://shiny-apps.stat.ubc.ca/FlexibleLearning/FirstBayes/Normal-Normal/

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License information is optional on submission but will be required for posting in the repo:

• LICENSE: CC BY-NC-SA 4.0

The following information is optional:

• LINK TO REPOSITORY: https://github.com/GiankDiluvi/first-bayes-r
• LEVEL OF DEPLOYMENT: Ready for use
• E-MAIL ADDRESS: gian.diluvi@stat.ubc.ca
• COURSES FOR USE: STAT 305
• PREREQUISITES:
  • Be familiar with the probability concepts of a random variable and conditional probability.
  • Know that, when making inference for Normally-distributed data with known standard deviation σ, a random sample is used to estimate the value of the mean, μ.
  • Be able to calculate and interpret confidence intervals for the mean of Normally-distributed data when the variance is known.
  • In the context of Bayesian statistics:
    • be familiar with the concepts of prior distribution, hyperparameter, likelihood, and posterior distribution;
    • know that the prior distribution should reflect your initial belief about the true value of the parameter;
    • be able to describe the roles of the hyperparameters in shaping the prior distribution.
• LEARNING OBJECTIVES: In the context of binary data with success probability of p:
  • Given data and a Normal prior for μ, calculate by hand from a formula the parameters of the posterior distribution of μ.
  • Given data and a Normal prior for μ, order, from largest to smallest, the prior mean of μ, the sample mean, and the posterior mean of μ.
  • Given data and a Normal prior for μ, obtain the posterior mean and variance of μ using an online interactive resource.
  • Compare and contrast the interpretation of a frequentist (1−α)×100% confidence interval for μ with a Bayesian (1−α)×100% credible interval for μ.
  • Explain the impact that different prior distributions have on the posterior distribution.
• ACCOMPANYING ACTIVITY: See StatSpace
• ADDITIONAL COMMENTS:

[cgtaylor1]

Thanks Gian Carlo for this submission too! It now appears in the Shiny Repo.